You say those two things are not mutually exclusive but the sentence, by itself, doesn't make that clear to me. I'd be more likely to read it as two unrelated questions if it was:
"Do you know if he has bank accounts abroad or if he travels abroad a lot?"

For some reason, the "whether" makes me think that an alternative to banking abroad is about to be presented and you may be thinking that travelling abroad a lot is some sort of solution to not having overseas accounts.

"Do you know whether he has bank accounts abroad or if he has local accounts?"

-"Do you know whether he has bank accounts abroad or if he travels abroad a lot?"
-"I don't know anything about his bank accounts, but I know that he does travel abroad a lot"

From this fragment of conversation I drew the inference that Person B has heard that the asserted traveller X has some foreign bank accounts, and has sought to verify their existence with Person A (the speaker).

I drew the additional inference that while Person A does not know whether X has foreign bank accounts, Person A thinks that if X does have them it may be because X travels a lot overseas.